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REPORT 



ON THE 



COMPRESSIYE STREMTH, SPECIFIC GRAYITY, 



KATIO OF ABSORPTION 



OF THE 



BUILDING STONES 



IN THE UNITED STATES, 



BY 



QTAy^GILLMORE 



LIEUT.-COL. CORPS OF ENGINEERS; BVT.-MAJ.-GEN., U, S. A.; AUTHOR OF "TREATISE ON 

LIMES, CEMENTS, ETC.; " "TREATISE ON COIGNET BETON AND ARTIFICIAL STONES ;" 

AND "TREATISE ON ROADS, STREETS, AND PAVEMENTS," ETC., ETC., ETC. 



OFFICIA 



TRANSFuR 




NEW YORK: 

33. VAN NOSTRANI>. PUBLISHER 

23 MURRAY STREET & 27 WARREN STREET, 



1876< 



.G-t8 



United States Engineer Office, 

New Torlc, August 10, 1875. 

General : I have the honor to state that my tests to determine the 
compressive strength, specific gravity, and ratio of absorption of the 
building-stones in the United States in most general use have been con- 
siderably extended since my report of July 30, 1874. The methods 
pursued and the results obtained, inclusive of those first reported, are 
embodied, and to some extent discussed, in the paper herewith sub- 
mitted. 

My assistant, Mr. Louis Nickerson, had immediate charge of all the 
experiments and tests made during the past year, and I am indebted to 
him for valuable suggestions and zealous co-operation during the pro- 
gress of the work. 

Yery respectfully, your obedient servant, 

Q. A. GrLLMORE, 

Lieut. Col. of Engineers^ Bvt. Maj. Ge7i., U. S. A. 
Brig. Gen. A. A. Huimphreys, 

Chief of Ungineers, U. S. A. 



REPORT. 



FORM OF SPECIMENS AND METHOD OF TESTING. 

Many of the specimens were delivered from the quarries in the form 
of cubes, measuring 2 inches each way, but the greater part have been 
wrought into form at Fort Tompkins. The desire has been to get 
average specimens, rather than to have the quarries picked for fine pieces, 
and it is thought that the attempt has been in general successful. Each 
cube was placed between two cushion-blocks of soft pine wood, 2 inches 
by 2 inches square, and slightly more than J inch in thickness, one on 
the top and the other under the bottom ; the grain of the wood being 
parallel in each to the other — though no difference was observed when 
this was changed, as regards amount of record. This arrangement 
caused the pressure to come more gradually upon the stone, and the 
cushions, becoming much indurated by the effects of pressure, to some 
extent took the place of the mortar used in actual building. 

For iron and wood, Hodgkinson has shown that trial specimens should 
be at least one and one-half times as high as the width of bed ; but 
stone, except when used as columns, is usually laid of less height than 
bed, and the cubical form of specimens adopted for the experiment 
affords sufficient security for the angular breakage which he proved to 
be necessary for a true result. This latter fact is corroborated by sub- 
sequent experiments. 

The cubes recorded in the general tables were brought to a true, 
smooth, and regular, but not a polished, surface. The granites and mar- 
bles, however, embraced in the tables under the head of '' Sundry special 
experiments," were carefully rubbed down to the border of a polish, 
because in these great homogeneity and fineness, especially of bed-sur- 
face, was rather desired than the true building-streugth of the stone. 
This latter plan undoubtedly increased the resistauc e* It is not, however 
a high valuation that we want for the general table, but a safe onej and, 
moreover, we desire to arrive at some knowledge of the resistance which 
the rock will have when applied in the usual manner in a wall. The mode 
used would seem to yield the truest answer to the experimental inquiry. 
Sandstones, of course, having no polish, give no difference of result 
from this cause. It must also be remembered that the general tables 
seek as nearly as possible to give the average strength of the average 



stone from any particular quarry, while the " Sundry special experi- 
ments," having been made with carefully picked stones, will give higher 
results from that cause. There may be some exception to the last 
remark in the East Chester marble, but, if so, that is believed to be the 
only one. 

Each specimen of all the kinds was carefully prepared by an expert 
stone-cutter, and the bed-side marked. These were then placed upon a 
table near the hydrostatic-press, used in such a manner as to mix them 
completely, and so prevent any inadvertent choice being made when 
they were picked up. They were there examined, squared, measured, 
and calipered, and then tested on bed or edge, under steel, wood, lead, 
or leather, as the routine prescribed. When placed in the press, each 
specimen was carefully centered to the axial line of pressure, and the 
power applied neither fast nor slow, but steadily. The records were not 
attempted to be made exact within 500 pounds — equal to 125 pounds per 
square inch on 2-inch beds and over. On smaller specimens than 1-inch 
cubes 100 pounds was made the limit of error. 

The weight of the movable parts of the press, with its attendant fric- 
tion and the pump-stroke — about 800 pounds in all — is to be subtracted 
from the records in the general tables, or 200 pounds per square inch. 
The subject of friction is discussed under the head of " Testing the press 
and gauges." 

aATjaEs. 

The press is supplied with two gauges, one indicating the pressure up 
to 100,000 pounds j the other to only 5,000 pounds. Both are connected 
by pipes with the lower end of the cylinder of the ram. Both gauges 
may be used simultaneously until tbe capacity of the 5,000-pound gauge 
is exhausted, when its connection with the cylinder is shut off by a little 
valve worked by a hand- wheel. Generally, in testing stones, the lighter 
gauge is not used. 

To check the working of the 100,000-pound gauge next to the press, 
another gauge of similar capacity was employed as a test-gauge. It is 
attached to the connecting-pipe, near to the pump. These gauges were 
manufactured in the city of New York, on a modified arrangement of 
Bourdon's principle. 

THE BREAKAGE OF STONE. 

The diagram accompanying this report shows sketches of eight sam- 
ples of stone. The first one, named homogeneous stone, is imaginary, and 
represents the general form of breakage of many sandstones and sac- 
charine marbles. The separate pieces shown are such as are usually 
picked up after breakage, although with other varieties of stone they 
are generally more angular. The other sketches of stone represent 
samples actually tested and broken. The numbers given with each ot 
them correspond with those in the tables. The position of the cube 
when tested is also stated, whether it was placed on " bed " or on " edge." 

Considering the infinitely-varied composition and character of all 
kinds of rock, it may be said that no material is less calculated to per- 
mit the establishment of special laws by a general form of breakage. 
It may be safely assumed, however, that more numerous and extended 
experiments, carefully and patiently conducted, will ultimately lead to 
the development of certain general laws relating to the behavior of 



stones under pressure, a knowledge of which will be most useful to the 
engineer and builder. 

Homogeneous stones seem, in most cases, to break in the following 
manner, (see Plate I:) The forms of fragments a and & are approxi- 
mately either conical or pyramidal, according as the stone is friable and 
of obviously granular structure, like sandstone and a few kinds of 
marble and granite, or compact, such as the true limestones and mosb 
marbles and granites. The more or less disk-shaped pieces c and d are 
detached from the sides of the cube with a sort of explosion, flying off 
in a more or less intact condition. In e and /, the stone is generally found 
crushed and ground to powder by the attrition of the larger fragments. 
Of course, this general result is modified by the nature and quality of 
the grain in the stone, and those other causes of irregularity which leave 
no two cubes of the same strength and condition, although they may 
have been cut directly apart from each other. 

This form of breakage occurs also in non-homogeneous stones broken 
on bed 5 but it must be remembered that here the modification must be 
taken into account which "grain" produces as against homogeneity, 
rendering the object liable to split in rectangular fragments. This fre- 
quently lengthens the cone or pyramid in stones on bed, and causes those 
set on edge to actually split in rectangular disks; the style of splitting 
being, of course, irregularly modified for different specimens. Sand- 
cracks, &c., in stones have also their influence in directing the pressure ; 
even the difficulty of determining the bed in some stones, after being- 
cut, may be a source of errors. 

SPECIFIC GRAVITY. 

The stones whose resistance to crushing-pressure had been tested 
were also experimented upon in relation to their specific gravity. In 
the course of these investigations, it was sometimes necessary to be 
content Avith rather small fragments of stone, of not more than 15 to 18 
pennyweight ; but generally they weighed from one to two ounces. 

On commencing this part of the work, some doubt was felt in regard 
to the best means of obtaining the correct displacement of porous stones j 
and all stones are more or less porous. It appeared evident that in 
weighing the stone first in air and then in water an error would be com- 
mitted by saturation. The first idea, to give the stone a coating of thin 
varnish, was abandoned, because, although the pellicle would be thin, 
yet no means could be taken to know precisely what its thickness was, 
or what it amounted to in its effects. The second idea, to soak the stone 
in very fluid resin, the pellicle to be washed from the surface before dry, 
was given up, because it was desirable to preserve the specimens iutact 
for experiments on freezing and other tests. 

The plan finally adopted was, first, to remove from the stone all loose 
particles, and round off all sharp corners and edges, bringing it, in fact, 
practically to that condition commonly known as water- worn. It was . 
then carefully weighed in air, immersed in water, and allowed to remain 
there until all bubbling had ceased, and its weight taken. It was then 
taken out of the water and weighed again, in its saturated condition, 
with the precaution of previously denuding the stone of superabundant 
water, by being compressed lightly in bibulous paper. The specific gravity 
is now found by dividing the weight of the stone, when perfectly dry, 
by its weight in the air after having been saturated, minusit^ weight in 
water. 



8 
This may also be expressed by the formula — 

W 

Specific gravity =^-—^^^ 

W representing weight of dry stone in air j W,, representing weight of 
saturated stone in air ; W, representing weight of stone immersed in 
water. 

In determining the specific gravity of stone, the weight of water was 
assumed to be 62J pounds per cubic foot. 

RATIO OF ABSORPTION. 

The term " ratio of absorption " simply expresses the weight of water 
absorbed by the stone as compared with the weight of the dry stone ; 
that is, if the stone when dry weighs 300 units, and the column of 
" ratio of absorption " shows the fraction g-^^^ it means that, by immer- 
sion in water, the stone will absorb 1 unit of it, weighing 301 units 
immediately after its removal from the water. 

The method adopted for ascertaining the specific weight of stone fur- 
nished at the same time the means to determine the " ratio of absorption." 
The weight of the saturated stone minus the weight of the dry stone 
gives, as a result, the amount of water absorbed. This might, perhaps, 
more correctly be called the "avidity of absorption," since it was 
limited to the period of bubbling. Some few stones, having been kept 
immersed in water for several consecutive days, showed a slight increase 
in weight. 

Since the capacity of a stone to absorb water has much influence on 
its durability, even during the warm season, and far more so in cold 
weather, the addition to the tables of this column was deemed advisable. 

TESTING THE PRESS AND aAUGES. 

It was deemed essential that the accuracy of the gauge records should 
be verified, and that the law under which friction was developed under 
varying pressure should be ascertained for the instruments actually 
used in testing the several kinds of stone, viz, Hoe's hydrostatic press, 
and Willing & Co.'s gauges. 

Two gauges were used. One of them, of 500 i:)ounds capacity', was 
extremely sensitive ; so much so that besides other useful results, it accu- 
rately indicated the power used in lifting and working the unloaded 
ram, leaving only the efficient power and friction to be accounted for or 
measured. The other and larger gauge has a capacity of 100,000 
pounds. 

From careful experiments made by Mr. J. Hicks, civil engineer, of 
Bolton, England, on rams of 4-inch and 8-iuch diameter, it aj)pears that 
the friction of a 4J-inch ram — the one used in these trials — is about uiue- 
tenths of 1 per cent, of the total pressure. 

Assuming the law of the increase of friction to have been definitely 
ascertained by these experiments for hydraulic presses generally, it was 
thought best to make some special trials with the one in use. These 
were several times repeated with approximately corresponding results.. 



The}^ were conducted in the following manner : It had been repeatedly 
noticed that small cubes of Michigan pine, when placed in the press 
and crushed against the grain, gave very uniform results. One-inch 
cubes, for instance, cut from the same piece side by side, crushed sud- 
denly at from 5,800 to 6,000 pounds pressure. An average obtained 
with 1-inch cubes of pine crushed separately was thus established. 

It was further ascertained by trials that sets of 2, 3, 5, 10, 15, 16, or 18 
1-inch cubes of the same material, placed in the press in succession, the 
cubes in each case being set side by side, though not within lateral 
supporting-distance of each other, gave proportional results — that is, 
the aggregate crushing pressure divided by the number of cubes, gave 
the average crushing strength obtained with the single cube, within a 
reasonable limiting error of, say, 500 pounds for large numbers. All 
the cubes in each set crushed suddenly and together. Several repeti- 
tions of this experiment gav^ similar results. It was also tried with 
2-inch and with 3-inch cubes, the aggregate crushing resistance — friction, 
of course, included — being always proportional to the number of cubes 
simultaneously crushed. The results of the more exact exiDeriments of 
Mr. Hicks were therefore corroborated, that the resistance from friction 
muvSt have been a constant percentage of the power employed, and not, 
as has been sometimes supposed, a differential increase. Indeed, this 
last-named hypothesis could not possibly obtain under the known laws 
of friction unless abrasion should set in between the lubricated leather 
13acking and the copper lining at between 1 pound and 6,000 pounds 
pressure per square inch. These were examined after a year's time, 
during which the entire power of the ram up to 100,000 pounds — equal 
to 6.290 pounds per square inch — had been repeatedly used. The leather 
was found to be natural and the copper glazed. Abrasion therefore had 
not taken place. 

There appears to be a singular and unfounded prejudice against the use 
of gauges for recording pressures, due apparently to the fact that several 
having proved incorrect, when properly tested, the results have been 
more or less widely advertised ; while the true instruments, constituting 
a very large majority of those in actual use, have remained unnoticed. 
It is unnecessary to say the same rule would banish the yard- stick and 
the pound-weight from existence, the first being often too short, and the 
latter too light. 

The three principal kinds of gauges are the spiral-spring gauge, the 
diaphragm- spring gauge, and the one used in all the experiments and 
tests herein recorded, known as the tubular- spring gauge. Its essential 
and characteristic feature is the tubular spring made of fine cast- steel, 
carefully bored, bent, tempered, and tested. The bending of course 
changes its original circular section to an elliptical one. As the fluid is 
forced into this, the greater pressure in the direction of the minor axis 
tends to change its sectional form toward the ciule, as the figure of 
greatest capacity, which of course it can never re ch until it becomes 
straight as at first, but which it approaches as the pressure increases, 
growing straighter at the same time. It is this straightening of the 
sirring which works the gearing and revolves the index-hands. 

The fact that this simple instrument can be made to register correctly 
upon a graduated dial, is full proof of the great delicacy of which it is ca- 
pable. It has certain advantages over the beam-scale for large pressures 
in this, that while the beam may be very correctly graduated for any ratio, 
say 1 to 100, and be very perfect for comparatively low pressures, yet it 
depends upon knife-edges, which, when we have raised our power, say 



10 

to 100,000 pounds, or higher, may begin to abrade, to sink into the 
plates supporting them, and to obtain another and an unknown hiw of 
friction. Therefore, although the ratio of 1 to 100, or that of any given 
beam, may be very perfect within certain limits of power, we cannot 
rel}' upon preserving that ratio, or rather we may be quite certain that 
it is not preserved when those limits are exceeded. The worst is, that 
we do not know to what extent the ratio of the beam is incorrect in 
recording high pressure. 

The gauge has all the pressure put upon it, when tested for accuracy, 
that it will ever have to bear. It requires simply to be tested up to its 
maximum per square inch, seldom equal to 8,000 pounds. Then, if the 
ram is never worked at over 8,000 pounds per square inch, which the 
safety-valve should insure for the safety of the cylinder, there comes no 
more pressure upon the gauge from a cylinder of 300 square inches than 
from one of 0.03 of a square inch. 

The ram used in these experiments having only 15.9 square inches 
area and 100,000 pounds power, the maximum pressure per square inch 
is 0,290 pounds, nearly, or 1,572^ pounds to the one-fourth of a square 
inch. The accuracy of the gauge-scale may therefore be thoroughly 
verified with a beam-scale known to weigh correctly up to 1,572J pounds 
and a hydraulic press having a cylinder of one-fourth of an inch sec- 
tional area. Of course the same gauge could be taken from the 15.9 
square inch cylinder and placed upon a 15.9 square inch cylinder, and 
the gauge-records multii)lied by 10 would give the true power used, the 
actual pressure on the gauge when weighing 1,000,000 pounds remain- 
ing precisely the same as when weighing 100,000 pounds on the smaller 
ram; that is, 6,290 pounds per square inch. However, any small error 
in the ratio of areas between the quarter-inch cylinder and the 15. 9-inch 
cylinder would also be multiplied by 10. To show how this might be 
reduced by scientific ai^plication to indefinitely small quantities is for- 
eign to the requirements of this paper. 

SUNDRY SPECIAL EXPERIMENTS 

Showing differences resulting from tlie use of various surfaces of irressure^ 
including steely tvood, lead, and leather ; differences in the compressive 
strength per square inch in different- sized cubes ; a7id of prisms of vari- 
ous heights in relation to breadth of bed. 

The first of these commenced with trials of the different results to be 
obtained in amount and mode of fracture between stones of same kind, 
and from the same block, all 2-inch cubes in magnitude, with different 
pressing surfaces. Hardened-steel faces, wooden cushion-blocks, about 
1 of an inch thick, cushions of lead, about ^V ^^ ^^^ ^^^^h thick, and 
afterward thin lace-leather, were introduced into the comparison. 

The specimens, as before observed, were taken for each experiment, 
from the same block, approximately yielding just the number wanted; 
were then most carefully brought to parallel beds by being ground in 
an iron frame upon a stone plane-table with sand and stone-dust, and 
were then truly squared. Theil'" surfaces, especially the beds, were on 
the borders of polish, as nearly ?i^ ttie? character of the stone allowed. 
When set out upon the table far iise; they were carefully mixed up, 
calipered, squared, and measuredj and the trial commencing with steel, 
was alternated regularly,* tlle.^ejednil stone being broken with wood, the 



11 



third with lead, and, in the second part of this series of experiments, the 
fourth with leather. This plan was varied on a few occasions only, 
when an evident flaw was observed, and the results omitted from the 
table. 

The instrument used to give security to the direction of the pressures 
was of the following description : (See Fig. 1.) 

P, is a cast-iron frame 1 
inch thick 5 B^ a 1^-inch cast- 
iron plate, to which it is fast- 
ened by lugs XX ; act, cast- 
iron mandrel with steel plate 
<j, IJ inches thick, secured to 
mandrel by 1^-inch steel screw 
wrought on back of plate j &, 
steel disk, 2 inches thick, set 
into same guides in which 
mandrel works. The mandrel 
and disk have 4-inch by 4-inch 
square faces, exactly parallel 
to each other and perpendicu- 
lar to guides. All the steel 
was hardened to straw color 
and then worked true. The 
mandrel is secured to the top 
beam of the press by wire 
cordage, the weight of the 
frame bringing that down 
easily after each breakage. 
The object O is placed truly 
under the center of the man- 
drel, through one of the four 
arched apertures in the frame, 
and the frame raised again by 
the pump, the stone being 
broken between the steel face 
c of the mandrel, and the steel 
disk 1). 

The top of the mandrel is 
segmental, so as to create no 
resistance to the true action of the guides, and a balk of wood, 4 inches 
by 4 inches by J inch, is laid upon this segmental top. This became 
hard and convex, but lasted throughout all the experiments. 

The phenomena of breakage by the steel and wood were nearly the samej 
a tendency in steel to make one pyramid of from 50^ to 60^ angle at base, 
rather than two of 45° each, was occasionally suggested, butnot sufficiently 
so to indicate a law. In both cases the form seemed to be of pyramids 
forcing out end pieces, and usually breaking them up. The end pieces 
from the wood were, as far as observed, slightly more prismoidal, and 
from the steel, more wedge-shaped. It is impossible to speak with cer- 
tainty, however, on this point ; tb£_te-me P, in both cases, confining 
the fragments, and thus secur^*g'much2^e^er destruction, by preventing 
their escape from the react><Hi fi^t^feOcessHhan when they were free to 
fly off at the moment of r 

With the lead, and sub 
entirely different. 





ther, the phenomena were 



12 

A dull thud, instead of a pistol-like report, and sometimes only the 
mere recoil of the gauge-needle, recorded the destruction — a destruction 
indeed which was complete. To the observing eye, vertical cracks burst 
instantaneously upon the sides of the specimen, about one-fourth of an 
inch apart, and all its cohesion was gone at once. Examination showed 
the fragments to be prismatic, with the greater dimensions parallel with 
the direction of the pressure, and with an unusual quantity of stone-dust 
intermixed. To be sure the central portions tended slightly to the pyra- 
midal form, but the fragments from the steel and wood trials are solid 
like the original stone, having little appearance of internal injury, but 
only of having been severed from each other forcibly. Those, on the 
contrary, from the lead and leather trials, appear to have been riven to 
their utmost recesses, and crumble between the fingers like wood-cinder, 
having been api)arently cleaved everywhere and in every direction in a 
manner, however, suggesting general parallelism with the line of press- 
ure at the initial moment of rupture. The very constitution of the rock 
is shattered when crushed in this manner. 

And it is not that the lead or leather appears to spread much. Tliey 
do not spread in all directions so much as the wood does in one. The 
phenomena seems to be this : that while one side is 
being made smooth by the steel plates the other ap- 
pears to be driven into the microscopic interstices of 
the rock, intruding by flowage — after the manner de- 
"^ scribed of metals in Trescas' experiments — then open- 
ing and splitting it by crowding pressures, and thus 
t from each end driving myriads of minute wedges into 

the rock, while the normal pressure causes a powerful 
^^: ' tendency to open in the middle. (See Fig. 2.) 

Lace-leather is of an extremely close texture, something like oil-soakecT 
rawhide, and retains in a great degree, like lead, the characteristic lines 
of the rock surface stamped upon it. Ordinary fibrous leather might 
have a different action. 

This course of special experiment was conducted in three stages. 
Stones of a well-known stable character, selected either from previous 
acquaintance or from knowledge otherwise derived, were used. In the 
first, Mill Stone Point granite was used, a stone of considerable hardness 
without brittleness, of weathering durability, and, from its clear fracture, 
evidently possessed of good tensile strength, even in proportion to its 
compressive resistance. In the second stage. East Chester marble was 
employed, and in the third, Berea sandstone of the blue-gray color. 

TABLE III. 

Table III shows very plainly the quantitative relations w^hich press- 
ing surfaces of steel, wood, lead, and leather bear to each other in the 
breakage of these several rocks. 

Now as the stones above mentioned were all relatively high in their 
respective resistances, and as it was evident that a very weak stone, 
crushing below the prt ssure i)er square inch at which wood, lead, or 
leather could exert idiosyncrasies different from those ot steel, would 
yield indifferently to either, it was naturally supposed that the difter- 
ences observed would rather converge as the compressive resistances of 
rocks decreased. 

The fact, however, that the characteristic breakage and the observed 
phenomena of yielding under wood were difl'ereut from those observed 



13 

with leather or lead, while all concurred in departing more or less from 
the quantitative results obtained with steel, suggested a continuation 
of the experiments so as to include rocks of the same kinds in name but 
of different characteristic. Directions were therefore given to obtain 
granite similar to that used as the inside lining of the capitol at Albany, 
and a marble similar to the Vermont marble, both of which were well 
known from prior experiments. These are both solid stones of fine 
grain, which take an excellent and beautiful surface, but are both, rela- 
tively to their kind, and certainly as compared respectively with the Mill 
Stone Point granite and East Chester marble, of a friable character. 
This may even be observed by attrition with the thumb-nail upon a 
fresh fracture, and they evidently possess less tensile, and therefore less 
beam strength, than the average rocks of their kind. The first, though 
well knit together, is micaceous in small spangles, the other granular 
like white sugar. 

These stones were then tried under precisely the same circumstances 
as those foregoing, with this exception, that several of them cracked be- 
fore breakage — an occurrence which did not happen to the others — and 
were, therefore, excluded from the record. 

TABLE III A. 

The result of these experiments shows a divergence instead of a con- 
vergence in relative results, and as the last-named, or softer, granite 
gave under steel, where its compressive power may be supposed to 
be tested, the same results as the first, it became suggestive that it 
was not the property of softness alone which had quantitatively changed 
the results between the two, under the rigid steel and the spreading 
wood. It was well, however, to test this by other experiments. There 
happened to be on hand a block of soft Sebastopol limestone or chalk, 
taken from the ruins of the Malakoff, which was, at least, soft enough to 
suit the purpose. There were also on hand three l^-mch cubes of a 
soft drab sandstone, and two specimens of sandstone from Massillon, 
Ohio. The first, or the chalk, crushes at about 1,000 pounds per 
square inch; the drab sandstone at about 4,000 pounds 5 andtheMas- 
sillon sandstone at from 6,000 to 8,000 pounds. 

2s ow if the softest of these stones gave the same results with steel, 
wood, lead, and leather, there could be little doubt that, so far as soft- 
ness was concerned, the results would not be divergent. 

A glance at Table III, A, will show that this is the case both with the 
chalk crushing at 1,000 pounds and the drab sandstone crushing at 
4,000 pounds per square inch; the former giving a uniform percentage 
of 100 for steel, wood, lead, and leather, and the latter the same for 
steel, wood, and lead, the trial with leather having been omitted. 

For the Massillon sandstone of the softest kind, crushing at about 
6,000 pounds per square inch with steel, we find the wood cushions 
giving results about 20 per cent, higher than those of steel. One of the 
four results obtained with steel plates, however, shows so much discrep- 
ancy, compared with the three others, that it may be rejected, and we 
may safely put steel and wood at 100 i per cent, each, lead at 90 per 
cent., and leather at 60 i)er cent. 

Here the difference between the lead and leather evidently results 
from their relative softness, the lead probably beginning to flow at a 
pressure of about 5,400 pounds per square inch, while the leather prob- 
ably begins at near 3,600 pounds per square inch. For the Massillon 
sandstone, crushing at 8,000 pounds per square inch, with steel, we 



14 

again find only a slight difference between steel and wood cushions ^ 
but here appears to be another boundary, where the lead plates again 
take their position at 85 per cent., (or half-way toward the normal 
amount at high pressure, 65 per cent.,) which seems to commence at 
about 7,500 pounds per square inch, from whence it remains constant 
to at least 25,000 pounds i)er square inch for steel, or 16,250 pounds per 
square inch for the lead itself. 

With Berea sandstone, Table III, we have the lowest results of the 
general average, steel giving 11,000 pounds per square inch crushing 
strength 5 wood, 10,000 pounds j lead, 7,500 pounds; and leather. 6,700 
pounds; the percentage being as follows: steel, 100; wood, 91; lead, 
65 ; and leather, 60. 

Down to these points, then, our deduced averages, taken from the 
table, are suf&ciently accurate for practical work ; and below these 
points, that is, among the softer and weaker stones, the peculiarities of 
the pressing surfaces are not developed, and we get about the same 
results, whether we use steel, wood, lead, or leather. 

It seems probable that the real cause of the divergent results obtained 
with the stronger and harder stones lies in the relations existing between 
their tensile and compressive resistances, and that the law under which 
those divergencies are disclosed will be expressed in functions of those 
relations. 

The properties of tensile strength, compressive strength, and hard- 
ness, though common to all varieties of rock, vary in their relations to 
each other among the different kinds within measurable and some- 
times within comparatively wide limits. 

It is practically known among builders that a stone may be very hard 
and yet be very inferior to another which is softer, if it is to be placed 
where any tensile or beam strain will come upon it. The subject will 
be further discussed in this connection after all the experiments, others 
of which bear some relation to it, shall have been described. 

TABLE IV. 

Other experiments were made, and appear in Table lY, regarding the 
difference between the resisting powers of stone — in this instance con- 
fined to one kind — at one-half, once, twice, and three times the bed-di- 
ameter in height. These, curiously enough, conform precisely to the spe- 
cific experiments made by Mr. Hodgkinson, and probably point to his fur- 
ther correctness in cases where the width of base is still less in propor- 
tion to the height. It will be obvious, however, from the number and 
completeness of these trials, that the general principle which he seeks 
to establish, namely, that the compressive resistance of rectangular 
blocks, when crushed between plates by a vertical force, is proportional 
to the horizontal area of the blocks, is entirely incorrect when the height 
is near or less than the bed-diameter. Kesults in this connection are 
more elaborately worked out in the two sets of experiments on the 
breakage of different-sized cubes with which this section concludes. 

With blocks having different relative heights the difference in the 
manner of breakage is very observable. 

Those in which the height is one-half the width of bed are in all cases 
simply crushed to powder under steel and wooil, and are more inclined 
to split in fine splinters, which easily become powder under lead and 
leather. 

Cubes break, as has been before described, into solid fragments under 
steel and wood, and under lead and leather split into as nearly a fibrous 
condition as stone can sustain a fibrous form. 



15 

Stones having a greater height than width of bed are 
partly split into large prisms by wood and steel, bnt more 
characteristically are broken across their heights in an 
obliqne plane, precisely as wood yields when, having greater 
height than diameter, it is pressed in a direction parallel 
with the fiber, as shown in Fig. 3. None of these latter were 
tried with either lead or leather. 

A more detailed description and discussion of Table IV 
will come into subsequent parts of this report, and therefore, 
to avoid a repetition of words, they are merely passed over 
here with brief notice. 

TABLE V. 




Fig. 3. 



The experiments recorded in Table Y were made on beams of stone of 
2 inches cross-section and 6 inches long, broken on supports 2J inches 
apart 5 -the bed being upon a long side, and receiving the pressure nor- 
mally. They were not quite satisfactory, because the first record was 
only approximately deduced, and because there were no specimens of 
the more fragile Vermont marble broken. These beams had partially 
flexible supports under them, made of soft pine, extending from the end 
If inches toward the center. A wrought-iron cylindrical rod, J inch in 
diameter, was laid across the top center, and the power applied to it. 
The results were as follows : Mill Stone Point granite. 4,000 to 4,500 j 
East Chester marble, 4,000 to 4,200 -, Keene (N. H.) granite, 3,300. 

From the known fragility of the Vermont marble in comparison, it 
could not have stood over 2,500, or, at most, 3,000, pounds. Accepting 
the larger number hypothetically, we should have Mill Stone Point gran- 
ite, 100 5 East Chester marble, 100; Keene (N. H.) granite, 77 ; Vermont 
marble, 75, as the relative beam strength of the stones compressed with 
steel, wood, lead, and partially with leather, in the first part of these 
discussions. 

TABLE YL 



The special experiments, Table III, with the different mediums for 
communicating the pressure — viz, steel, wood, lead, and leather — were 
made with stones in a fairly-j)olished condition, when polish able stones 
like granite and marble were used. The sandstones were rubbed to a 
fine smooth surface. Now, inasmuch as the general tables were pre- 
pared with stones that were not polished, and many of which were incap- 
able of receiving a polish, though all were carefully dressed to a smooth 
and even surface, and crushed between disks of pine wood, some varia- 
tions of results were to be apprehended from differences in the condi- 
tion of the surfaces of the cubes to which the power was applied, even 
though the same compressing medium was employed. 

Some closing trials, recorded in Table VI, were therefore made, in 
order to obtain requisite data for making a connection between the 
special results and those recorded in the general tables. It seemed to 
be fair in this case to use as many different kinds of stone as practicable, 
rather than to divide the same number of experiments among several 
specimens of the same kind; because the general tables, comprising care- 
fully-selected average stones, rather than fine specimens, are really the 
basis upon which all the others depend ; and, as the general tables afford 
us numbers of trials already made with practical beds, which could be par- 



1 G 

alleledwith polisbed stones of the samekind.itwasconcludedtousethein. 
One difficulty, however, remained : specimens could only be replaced, as 
regards certain kinds of eastern rock, which were at the head of the list, 
and several of these had, in the general experiments, cracked long before 
breakage, and thus broken at a disadvantage. The difficulty was obvi- 
ated — nearly so, at least — in the following manner: extra fine speci- 
mens obtained for the second or special trial were carefully polished, all 
breakages from cracking were thrown out, and these were compared 
only with the best specimens of similar kinds in the general table. The 
difference appears to be about 25 per cent, in favor of polished surfaces, 
but is probably a little less. Sandstone, being incapable of polish, and 
consequently always similar in surface, gave in all the trials no appre- 
ciable differences. 

One object of these experiments being to connect together, as closely 
as possible, all the various trials that have been made by experimenters, 
in which various substances have been used as pressing- surfaces, it was 
also necessary to add another series, on the strength per square inch of 
different-sized cubes ; this selection of form being made because almost 
all experiments had been conducted with cubes, whatever the size used; 
and because reason, experience, and precedent seemed to concur in the 
advantage of that selection. 

Among the experiments of Mr. Hodgkinson which are of peculiar 
interest are those relating to the question of a changing strength, as 
the bed-surface of any substance increased in area. For this he used 
teak-wood in cylinders ^ inch, 1 inch, and 2 inches diameter, and in 
each case twice the diameter in height. It will be recollected that he 
thus obtained results showing the ratios of strength to be 1 : 4: 16: or, 
in other words, the same resistance per square inch of bed-area. 

Kow, on the contrary, 1-inch, 2-inch, and 3-inch cubes of Michigan 
pine, crushed against the ends of the fiber, daring the course of these 
trials, gave a considerable increase in strength per square inch as the 
size of the cubes was increased. This test with pine was only intended 
to be preliminary to similar trials with stone, should the results seem to 
justify the necessary expense thereof, and is not of itself especially 
worthy of record. It only gave a direction to further experiments. 

Eeferring to Tables II and iy,and taking them in connection, we find 
by the former that a 1-inch cube of bluish Berea sandstone, broken under 
steel, sustains 9,500 pounds, and that consequently four separate cubes 
of that size crushed side by side would just sustain four times as much, or 
38,000 pounds. Yet, when in one piece, forming a slab 2 inches by 2 inches 
by 1 inch, or, so to speak, when they are connected together by their own 
substance, it actually sustains nearly 76,000 pounds, or twice as much 
as the set of four 1-inch cubes; and when the height is increased into 
the form of a 2-inch cube, it sustained nearly 50,000 pounds, or less than 
two-thirds as much as the slab, although one-third more than the set of 
four 1-inch cubes. When the height is further increased to twice the 
width of base, it sustains only 44,000 pounds, or fully one-tenth less 
than the 2 inch cubes. 

The general cause of these differences is readily obtained from the 
course of the strains, which — if we suppose them for simplicity to act at 
an angle of 45° in the stone, and the material is known, under the same 
circumstances of crushing, to yield under a constant angle — do not pro- 
duce results in the cube in the same manner that they do in the slab. 
(Figs. 4 and 5.) 

The lines in the cube (Fig. 4) have a tendency to ])ush out the mate- 
rial lialf-way up the sides at a b, while they are restrained in the slab 



17 



(Fig. 5) by the frictional resistance of the steel plates to the lateral 
motion of any parts of the specimen. 





Fig. 4. 



Fig. 5. 



I^ow it is evident from the relations of hard slabs, broken by wood 
and steel, that these differences should be decreased with wood cushions 
by their yielding to the pressures a' and &', resolved horizontally. This 
is also" evident from the same table, because slabs and cubes of the 
same bed-area broken by steel give differences of 50 per cent., while the 
difference between slabs and cubes of the same bed-area, broken by 
wood, is only 5 per cent. And still further, we see that as we rise in 
the height of the prism broken by steel, so that the side-strain cannot 
be absorbed by the very rigid metal, the closer become the relations 
between prisms of different heights. At the same time the results 
obtained with wood and with steel cushions approach each other. 

Could it have been foreseen in an early stage of these trials that the 
results, while fully corroborating those of other experiments so long as 
their methods were precisely copied, yet departed from them very 
widely by change in the form of the specimen, (so widely, indeed, as to 
be in practical opposition thereto,) they would have been carried much 
closer to exhaustion. 

Nor are we debarred from a very close determination of the corre- 
sponding relations, when stone blocks of various forms are crushed 
between disks of wood. In Table I we find that a 1-inch cube of the 
yellowish-gray sandstone breaks at 7,000 pounds. Four of these placed 
side by side would therefore require 28,000 pounds to crush them. But 
one 2-inch cube breaks at nearly 36,000 pounds, and as the difference 
between a cube of this size, and a slab of the same bed but only half the 
height, both of the same kind of stone, though stronger, and both 
crushed under wood, is only 5 per cent., (Table lY,) we may place the 
2-inch by 2-inch by 1-inch slab of yellowish-gray sandstone at 38,000 
pounds compressive strength. The difference of resistence, therefore, 
between a set of four 1-inch cubes, crushed simultaneously side by side^ 
and four 1 inch cubes, horizontally joined together by its own material, 
or, in other words, a slab 2 inches by 2 inches by 1 inch, is about 10,000 
pounds, the slab being nearly one-third stronger. 

Having thus proved that there is a difference, we will now proceed to 
estimate the phenomena of that difference, and then to show its quanti- 
tative relations. The following data are taken from Table lY : 

II-2 



18 



-W3 © 

Si 


Dimensions of prism. 


How broken. 


g 

s 

11 
f 


u - 

hi 


i 


2 inches by 2 inches by 1 inch 


Under steel 

do 


7.5, 888 
34, 643 


18, 972 
15, 397 


1::::.:::: 










4 


3,575 










1 


2 inches by 2 inches by 2 inches 


Under steel. 

..do 


49, 137 
25,350 


12 284 


1 


1^ inches by 1^ inches by 1^ inches 


11 266 




Difference per square inch 






1 .. 


1 018 












2 


2 inches by 2 inches by 4 inches 


Under steel 

do 


43, 980 
*24, 000 


10 995 


2 


a inches by 1 J inches by 3 inches 


10 666 




Difference per square inch 






2 


329 













* Deduced from 1^-inch cube, and the 1^ inch by IJ inch by 4 inch columns, Table IV. 

The results teach us that slabs increase in resistance per square inch 
greatly as their surfaces are increased. That cubes increase somewhat 
more slowly, about one-third or one-fourth as much. That columns in- 
crease within limits which may be covered by the natural inaccuracies 
of experiment, certainly not more than one-fifth of the cubic increase, 
or one- tenth of that of the slabs. 

Again we accord with the specific experiments of Mr. Hodgkinson, 
while we plainly contradict the law *' of the equality of intensity for all 
areas of pressure," which he deduces therefrom, in so far as he claims 
it to be general. 

From this result the following experiments, which conclude this con- 
nection, may now be discussed. 

TABLES I AND II. 

Berea sandstone from the same ledge and stratum, being comparative- 
ly a very uniform stone for a soft one, was selected for these trials. 
There appear to be three kinds of Berea stone : one a rather soft, yel- 
lowish-gray stone with orange bed-lines, probably containing hydrated 
sesquioxide of iron as a pigment. Another, drab-gray in color, rather 
harder, which was not used except in the general table, and which seems 
to run into the two others, and to be less uniform in strength than either 
of them. The third, a bluish-gray stone without bed-marks, harder than 
the others, and of much more compact texture. 

The stones from* the test^, of which the lower curve Plate II (Table I) 
was constructed, were broken with wooden cushion-blocks, one-sixteenth 
of an inch thick for the ^-inch cubes, and increasing by steps to a little 
over three-eighths of an inch for the 4-inch rube. By an accident all 
these were not taken from one block, though all were of the yellowish- 
gray variety of stone. 

The stones which produced the upper curve, Plate II (Table II) were 
broken with steel plates, were all from the same block, and of the blu- 
ish variety, which, being strong, restricted the upper limit to 2J-iuch 
cubes, as the largest that the press would crush with safety. 

The sides of the cubes, increased one-fourth of an inch at each step, 
are shown in inches on the abscissa or horizontal line X. The vertical 
lines Y show the crushing-pressures in pounds per square inch of bed- 
surface, that is, the total resistance of the cube in each case, divided by 
the number of square inches in one of its faces. 



The form of the theoretical curve is that of a cubic parabola, with the 
equation 

y = ^/ XX a 
iu which a is the cube of the unit-strain, or the pressure in pounds on 
a 1-inch cube which crushes it. The results were worked out from the 
averages given by the first trials with wood-cushions ; those afterward 
made with steel being carried on to contradict or corroborate them. 

In the lower curve, a is the cube of 7,000 pounds, the force in round 
numbers required to crush a 1-inch cube of the yellowish stone under 
wood ; and in the upper curve, a is the cube of 9,500 pounds, the force 
necessary to crush a 1-inch cube of the blue kind under steel. 

The equation for the lower curve will therefore be, 

y = 7000 X \^'jo 
and for the upper one, 

y == 9500 X V^ 
X being the side of the cube expressed in inches, and y the pressure in 
pounds per square inch of bed-surface at the moment of crushing. 

It will be observed that the lower curve, constructed on the experi- 
mental results given in Table \a^ makes only an approximative running 
in relation to the theoretical curve constructed according to the calcu- 
lated results of the same table. The upper curve almost coincides in 
seven average points with the calculated curve ; one point — that given 
by the 2J-inch cube — indeed, considerably falls short of its computed 
position. An examination of Table II, however, shows that the 2|-inch 
cubes at this point broke with nearly the same absolute pressure as 
the preceding 2J-inch cubes. We may conclude that these specimens 
came from a soft vein in the block, and that this discrepancy may be 
neglected in view of the close approximation of the other points. 

While the co-efficients, 7,000 and 9,500, will of course be different for 
different kinds of stone, they will also vary more or less for each kind 
of stone, according to the nature of the cushions between which the 
cubes are crushed. But these data once given, the formula would seem 
to afford a ready means for estimating the probable resistance of various 
sizes of building-stone in the form of cubes. 

It appears, then, that, at least within certain, limits, the compressive 
resistance of cubes per square inch of surface under pressure increases 
in the ratio of the cube roots of the sides of the respective cubes ex- 
pressed in inches. Thus it will be seen from Table I a that the actual 
resistance of a ^-iuch cube, expressed per square inch, was about 6,080 
pounds, (5,558 pounds by calculation.) Now, according to the formula, 
a cube of eight times the length of side of a ^-inch cube, in other words, 
a 4-inch cube, should be crushed under a pressure of -^ 3 x 6,080 pounds 
per square inch, or 12,160 pounds. Actually it was crushed by 11,720 
pounds, the difference being only 1 i)er cent. The calculated pressure 
per square inch of a four-inch cube is 11,112 pounds, being likewise a 
difference of but little more than 1 per cent, from the observed pressure. 

The conclusion is, that having ascertained from an average of several 
careful trials the crushing-resistance of a 1-inch cube, an 8-inch cube of 
the same kind and quality of stone, crushed between the same sort of 
cushions, should show twice as much resistance per square inch of sur- 
face pressed as the 1-inch cubej while to produce three times the unit- 
resistance per square inch, the cube must have sides of 27 inches. This 
conclusion was, however, not borne out by' experiments made in the 
II— 3 



20 

Brooklyn navy-yard, referred to further on. The discrepancy might, 
perhaps, be largely accounted for by the want of uniformity of grain and 
texture in comparatively large blocks. It was subsequently ascertained 
that the accuracy of the testing-machine used was by no means assured. 
The results may, therefore, be set aside for the present. 

In regard to the application of the formula above given, there will 
arise the question as to the relations which exist under it between a 
number of combined cubic inches and a single isolated cubic inch. The 
formula for the pressure on each square inch of bed being 



y = y XX a 

and the total bed-surface of a combined cube, having sides x inches in 
length, being x^^ the whole crushing-power acting on the cube will, 
therefore, be 



The pressure received by each of the individual cubic inches, of which 
we imagine the whole cube to be composed, considering that the whole 
mass contains a number of cubic inches represented by x^^ is, therefore, 
equal to — 



x^ y/x X a y 

^ X S/x X a = =- 

X^ ^ X X 

This result shows that while the crushing-resistance per square inch 
of bed-surface increases as the size of the cube is augmented, each indi- 
vidual cubic inch of the whole mass decreases in its power of resistance. 
For instance, by examination of the computed values in Table I a, we 
find that the crushing-resistance of 1-inch, 2-inch, 3-inch, and 4-inch 
cubes per square inch are set down at 7,000, 8,820, 10,095, and 11,112 
pounds, 1 espectively. But the average crushing-resistance of each 
individual cubic inch of these same cubes will be in the rapidly descend- 
ing ratio of 7,000, 4,410, 3,365, and 2,778 pounds. 

In this connection some discussion might be entered into concerning 
the ratio existing between the actually destroyed portions and the 
solid fragments of the cubes, as shown in the sketch of " homogeneous 
stone," Plate I, but it is omitted on account of the length which this 
report has already attained. 

From the curves it follows : That if certain cubes of unit dimensions 
are built together, with cement equal to their oivn substance, into a cube of 
larger dimensions and of homogeneous strength, the resistance to compres- 
sion per square inch of bed surface increases as the halfordinates of a cubic 
parabola. 

As before mentioned, it is doubtful whether this law continues into 
the ordinary dimensions of building-blocks, and experiments in Table IV, 
where columnar side-lorce is taken into consideration, suggest, even 
. shouhl it apply to large blocks, that where the height of the wall is 
twice as great as its smallest horizontal dimension, no increased strength 
would be conferred on the wail, even if the cohesion of the mortar to 
the stone and its tensile and compressive strength were equal, respect- 
ively, to the tensile and comi)ressive strength of the stone itself, condi- 
tions vvhich never obtain. 

In i)iactice, the law would apply only to the individual blocks, having 
a height not much, if any, greater than the width of bed ; but whether 
these are of restricted sizes, and, if so, what the largest size is, beyond 
which the formula fails, has not yet been determined satisfactorily. 



21 

The large cubes to which reference has been made were crushed at 
the Brooklyn navy-yard, with a 2,000-ton press, in which was a gauge 
subsequently tested to our test-gauge. Five 11-inch cubes of Berea 
sandstone were crushed. Whether the action of these stones was anom- 
alous from specific causes, or whether from general causes, the law of the 
increase of strength per square inch fails at a particular value of x, it is 
impossible to say positively without additional trials. But these large 
stones broke invariably by splitting vertically in large flakes or sheets, 
varying from 2 inches to ^ of an inch in thickness, and quite reg- 
ular over the greatest part of their surfaces of fracture, especially 
the thinner ones. It is by no means impossible that all rocks have, 
more or less, a series of joints, somewhat resembling slaty cleavage, 
along which they open more easily than in any other direction. As the 
thickness of these joints belongs to the material, and is not changed by 
the size of the specimen, it follows, plausibly enough, from an exami- 
nation of the annexed Fig. 6, and from the ordinary laws of 
the bending of columns and sheets transversely to the line 
of pressure, that the two sheets forming the small cube a, 
for example, having a height equal to only twice their width, 
will be crushed in combination rather than bend singly. 



while those of the large cube A, having a height equal to Fig. 6. 
eleven times the width, will bend and separate rather than crush, and being 
thus bent and separated, will fly off consecutively from the block. This 
was the phenomenon displayed by the 11-inch cubes referred to. They 
crushed at somewhat less recorded resistance per square inch of bed 
than 2-inch cubes of the same stone. All the circumstances of their 
breakage, however, were very unfavorable, the accuracy of the testing 
machine, even, being extremely doubtful. 

MODES OF EXPERIMENT DISCUSSED. 

It was deemed proper, in my first report "on the compressive strength, 
specific gravity," &c., of various kinds of native building stone, submit- 
ted with my letter of July 30, 1874, to refrain from any positive enunci- 
ation of principle, for the simple reason that the experience gained in 
using disks of wood under and over the samples did not seem sufficient 
to justify a claim for special advantages in this departure from the 
usual methods of experiment. Indeed, there was a dbsire to elicit criti- 
cism upon what had been done, rather than to give prominence to the 
method of doing it. The question of the entire adequacy of this meth- 
od for securing the object in view, and the reasons for adopting it, will 
be discussed as briefly as possible in this report, i^ot that this or any 
other manner of trial may be claimed to be the very best that can be 
devised ; but only that, while admitting the necessity of obtaining the 
compressive strength of specimens for special and practical purposes, it 
may be also claimed that it is only by placing these specimens as nearly 
as possible under the exact circumstances which most occur in the com- 
bination of vertical and side strains, developed in actual masonry, that 
we can reach, or make much progress in, a solution of this useful prob- 
lem. 

No one can doubt the usefulness of experiments to obtain the crush- 
ing and tensile resistance of cast or wrought iron, or steel. But having 
these — the compressive and tensile strengths of cast iron, for instance — 
and combining them together to calculate the strength of a rectangular 



22 

beam, we should find on testing the beam that we had wasted a large amount 
of material, and that it was much stronger than the results obtained by 
calculation indicated. Besides, therefore, the abstract knowledge of 
crushing-strength which we possess, we must also, by some series of 
experiments, combine these and other relations so as to learn whether, 
as in the case of beams and columns, there may not be new forces born 
of the combination, an acquaintance with which would materially add 
to our constructive power. 

Connected with our subject, and therefore of special interest, is the 
discussion made by Mr. Hodgkinson in regard to the breaking of short 
prisms for the purpose of finding the exact crushing-resistance of cast- 
iron. Discovering in his earlier examinations that when these were 
shorter than their sectional diameter they resisted to a far greater ex- 
tent than the metal could do as used practically, he thenceforth ignored 
such tests, beyond the simple fact of their existence, and confined his 
trials to prisms having a height of one and one-half the diameter or 
more, because there the material gave ivay by the same laws, and in the same 
manner, as it does when used to guard human life, or secure valuable xirop- 
erty. In these trials he first discovered the angular breakage of material, 
and the law of constant direction, under the same conditions. 

In making experiments on stone, it would, from the different nature 
and uses of the material, be evidently improper to follow blindly the 
modes used for cast iron. Here are no flanged girders or hollow columns 
to form culminating points of inquiry. Yet in principle we have the same 
necessity for reasoning directly toward the end to be ultimately attained, 
to watch carefully the character of the material, its mode or modes of 
yielding, the uses to which it is daily put, the peculiar stresses and 
strains which come upon it, and all this, not as an individual stone which 
our curiosity has induced us to investigate, but as the integral part of 
some vast natural structure taken down little by little, and transform- 
ed into smaller artificial edifices. 

In regarding the idea of a crushing-force, the mind is too easily led to 
conceptions of vertical lines of strain, reaching directly from the weight 
at the top to the foundation at the bottom. It need hardly be said to 
engineers that such strains have existence only in the pages of mathe- 
matical applications, and could only be possil3le under the hypothesis 
of a film of material only 50^000000 ^^ ^^ mQ\i, or one molecule thick. 
So soon as another film is superadded, oblique arrangements of molecule 
and strain would intervene underpressure, and tangential stresses would 
be developed. If this were not true, there would be no such pbenomeua 
as angular breakage, spreading under weight, nor any need for bond on 
masonry, but blocks of stone, or brick, or any materials, piled vertically 
one upon another, would, under a destructive load, be gradually com- 
pressed into a smaller volume, within the limits of their original horizon- 
tal dimensions. 

Thus in crushing an individual specimen, the principal lines of strain 
may be symbolized by the lines AB, BD, and AC, CD of the annexed 
figure (7.) A, being the crushing-force, D the resistance, and B and 
the side-pressures. The angle of 45° is used only for 
sitiiplicity, and because it is the maximum. Now, these 
strains have a tendency to i^ush out the material at B 
and C, and cause either spreading or angular break- 
age, according as the substance is soft and cohesive 
or hard, granular, and brittle, while the resistance is at 
the same time increased or decreased by the rigidity', or 
yielding, or pushing of the foreign surfaces which press 




23 

upon tbe object on the top and bottom planes at A and D. The nature 
of these snrfaces, then, becomes a matter of great moment, as does also 
the height of the specimen in relation to its diameter, because each 
material has different uses in the arts, and because we know that the 
lines of strain have constant angles for each kind of material — depend- 
ing to some extent, no doubt, on molecular arrangement — when crushed 
under the same circumstances. 

In good masonry, in which the strength of the structure depends upon 
material and bond, stones should never be used of greater height than 
the breadth of the bed. Our experiments, then, unless we should pur- 
posely test for columnal strength, would not be made on objects over a 
cube in height. Bn t early experiments showed that the cube gave quite 
sufficient opportunity for the natural angular breakage of stone, and 
subsequent trials with homogeneous kinds proved that, while slabs less 
than a cube in height, pressed by unyielding surfaces, gave much greater 
resistance than cubes, those higher than the cube to the limit of 
nearly three times the width were but little if any decreased in resist- 
ance by increased altitude. The cube, therefore, was the form depended 
upon for specimens; a determination carried out with greater satis- 
faction from the knowledge that other experimenters with stone had, for 
perhaps other reasons, arrived at the same conclusion. 

Probably the first idea which would strike the investigator would be 
to make the pressing-surfaces of the same kind of stone as the speci- 
men to be tested. But this surface must not be continuous, because we 
never build (except when forming a detached column, where each course 
is a single block) by placing one stone directly upon the top of another. 
Necessarily, for the strength of the structure, we introduce what is 
called bond; we have therefore headers and stretchers^ and over and 
under each stone there are usually one or two joints, free in dry ma- 
sonry, or filled with adhesive mortar in most works. 

So, to arrive at this point, each object would have to be built in with 
others of its kind, in imitation of usual structures, and we could then 
calculate the several strains, and estimate the various strengths of the 
component parts of our experimental structure by the stresses which 
should be determined for them. This would be an expensive mode., 
w^ould be difficult to tabulate, and would probably have its attendant 
errors, to be eliminated with great toil. We have then only one course 
left; we must study the strains which shall come upon the stone in 
masonry, and approximate to them as closely as possible in our tests of 
the material. 

In the general case, we must consider that stone blocks are employed 
for building purposes in the form of a wall, and that if such side- 
strains as we have mentioned as coming upon an individual block 
should also be similarly developed in the structure, it would, with excep- 
tional cases, strain the stone seriously only in one line. 

If a wall be built high over a lintel and the lintel be then removed, no 
matter in what manner the wall is bonded, if there be a close juxtapo- 
sition of parts, so that the vertical and side stresses may combine them- 
selves into oblique resultants, the masonry above the opening will not 
fall away in vertical lines from the top of the wall to the jams which sup- 
ported the lintel, as it would if only subjected to vertical stresses, but 
jwill arch itself over the aperture and support the superincumbent 
-courses. The magnitude of the side-stress, then, might be computed 
from the profile of the parts remaining. 

Again, the ordinary pier, such as those too commonly built upon our 



24 

couuty-roads and sometimes upon railroads, when yielding by incapacity 
to uphold the weigbt placed upon it, gives way, as in Fig. 8. At the 
I top and bottom the width of the opening^ is zero, 

,^ f ^, but it widens in the middle of its length. It may 

occur in the center if the work is of nearly uniform 
character, or at relatively weak points where it is 
not; but the side-strain is always evident, the two 
sides of the pier being deflected horizontally where 
the greatest strain comes. 
_ Now, this side-deflection is not produced as in an 
elastic beam mainly by the elongation of the outer 
line and the depression of the inner one, but is the 
Fig. 8. result of a shearing strain alone, the slipping of the 

courses past each other; such an action, in short, as is sometimes cor- 
rected against in arch-thrust, and other important cases, by a vertical 
bond holding each two courses together. Such strains as that shown in 
the pier have torn stones asunder. In fact, stone is more likely to yield 
in this manner, where the work is well put together, than by crushing 
under vertical pressure. 

For really good masonry, the danger may be approximately calculated. 
The stones in Fig. 8 have obviously slipped, because the "bond-grip" 
or "bight" was less than the tensile strength of the stone. 

Take a good piece of granite masonry as an example, which shall be 
of first-class design, arrangement, and workmanship, and shall so far 
satisfy the general definition of good masonry, viz, " the smallest quan- 
tity to sustain a certain duty" that the vertical stress and the compress- 
ive resistance of the stone shall balance each other, and tliat the side- 
strains shall also balance the tensile resistance^ and either of these the 
" bight" coming from friction. 

Let us now assume that the granite block A, of Fig. 8, has been 
pulled by the side-strain from between the stones a and h ; that the wall 
is built of cut stone, without mortar ; that the transverse section of A 
is, for the sake of simplicity, 100 square inches ; and that its bond 
between a and h has the same area. Now, taking granite at its highest 
tensile strength, say 3,000 pounds per square inch, and we have for the 
resistance to side-strain, by the tensile strength of the stone, 300,000 
pounds. Taking the friction of stone on stone at 0.7, and the vertical 
force which overloads the wall at only 5,000 pounds per square inch, and 
we have 100 x 5,000 x 0.7 = 350,000 pounds. So the stone, if in a dry 
wall, would break rather than move. It is scarcely to be expected that 
good mortar or cement would decrease the strength of the bond, or that 
sandstone, which has nearly the same frictional resistance as granite 
and a tensile strength of less than 1,000 pounds per square inch, woukl 
give a better wall. 

It is true that stones seldom give way in this manner, because good 
masonry seldom yields at all. Indeed, stone seldom yields by crushing. 
It is a cheap material, and the security is therefore kept high, but the 
benefit and object of experiment is to find the line of danger, and to 
know its true direction we must find its position at more than one 
point. 

We have already chosen cubes for form, because they sufficiently 
secure the natural angular breakage which comes upon the single stone, 
and we have now, from the data exposed, to clioose some surface of 
pressure to be ai)plied to that cube, so as to imi)art to it, as nearly as 
possible quantitatively, the oblique pressures which each stone receives 



25 

from its combination in the wall. iS"ow, wood, which of all substances 
spreads its maximum in one direction, and but very little transversely 
thereto, would seem to serve our purpose. A few remarks on this point 
will suffice. 

From Mechanics of Engineering, (Mahan's Mosely,) we have the 
following for the friction of different substances, at rest, which enter 
iuto our inquiry : 

Co-efficient of friction of plane surfaces when they have 'been some time in contact. 

Calcareous oolite stone upon same 0. 74 

Hard calcareous stone (muschelkalk) upon oolite 0. 75 

Brick upon calcareous oolite 0. 67 

Muschelkalk upon same 0. 70 

Calcareous oolite upon muschelkalk 0. 75 

Brick upon muschelkalk 0. 67 

Calcareous oolite upon calcareous oolite, coating of mortar 0.74 

Smooth freestone upon same, dry 0.71 

Smooth freestone upon same with fresh mortar 0. 66 

Hard, polished calcareous stone upon same 0. 58 

Hard, polished calcareous stone upon same with rough surfaces 0, 78 

Well-dressed granite upon rough granite 0. 66 

Well-dressed granite upon rough granite with fresh mortar 0. 49 

Oak upon calcareous stone, upon end of fiber 0. 6.3 

Oak upon muschelkalk, fibre flatwise 0. 64 

Pear- wood upon stone, ( Wiesbach) 0. 64 

It is, of course, to be regretted that the friction of pine- wood upon 
stone generally could not be obtained. But the general course of the 
table leads us to take it as a near approximation to the result we seek, 
especially as the i3ine-wood is, under the pressure employed, as hard 
and tough as oak or pear-wood. Then, too, it may be thought by some 
that, as the wood acts by spreading, the friction of motion would 
be the true state to use, which would reduce the friction of wood on 
stone to 0.38 or 0.40, without materially altering that of stone on stone, 
either dry or mortared. But it must be borne in mind that this small 
motion of spreading against the grain of the wood, by searching the 
interstices of the stone, should rather increase the friction than other- 
wise, and is different from the motion of translation of the whole block, 
which would diminish the force by which the molecules of the two ma- 
terials attach themselves to each other. But even if there should be a 
quantitative difl'erence, within bounds, it must be allowed, even if it 
cannot be measured, because, of all substances, wood is the best, if not 
the only one available, for giving the side-pressure in one direction, 
which is what we set out to attain. We know that the surface of the 
wood contiguous to the stone has little or no motion, and that only the 
internal layers, especially the center ones, move with any freedom. The 
friction, therefore, while it will be somewhat less than that given in the 
above table, will not be as low as 0.38 or 0.40, the friction of motion. 

Direct experiments in crushing blocks of different kind of stone be- 
tween cushions of different material, viz, steel, wood, lead, and lace 
leather, were carefully made, in order to determine the ratio of resistance 
under the various conditions thus imposed. The steel plates were of 
sufficient thickness to be perfectly rigid under the greatest pressure to 
which they were subjected. Their effect is to hold the stone together 
by their frictional resistance to lateral spreading. 

The wood — sheets of pine, a little over a fourth of an inch in thick- 
ness — spreads in one direction with comparative freedom, and thus 
throws a tensile strain on the block. 

The sheets of lead and lace leather appear to be driven iuto the inter- 



26 



stices of the stone, and, with slight spreading in all directions, to split it 
into vertical prisms as wood is split by wedges. (See sundry experiments.) 
The first series of the experiments, Table III, was made on Millstone 
Point granite, East Chester marble, and blue Berea sandstone, all no- 
tably tougli and first-class building-stones of their kind. The ratio 
obtained for the three taken together, omitting small fractions, was as 
follows, the leather being tried with the sandstone only: 

Steel, 100 5 wood, 94 ; lead, 65 j leather, 60. 

The second series was made upon stones having nearly or quite as 
compact and close a texture on the ground-surface as the foregoing, 
but were more friable upon the surface of fracture and evidently pos- 
sessed less cohesive and tensile strength. These were t^e Keene {^, 
H.) granite, used for the inside lining of the new State-house at Albany^ 
and the Vermont marble, a clear, smooth, and delicate-looking stone. 
From these the following average ratio was obtained : 

Steel, 100; wood, 82. x ; lead, Q5.— ) leather, 63.5. 

This showed a material change for wood alone, which might occur 
either from the more or less tensile strengths, or have some connection 
with the hardness or softness of the stone. That it was not the latter 
must appear from the following discussion and corroborative experi- 
ments : 

If it were the softness exclusively of the latter stones which produced 
this diminished result with wood-cushions, the difference would increase 
as the softness increases, but it is easy to perceive that a rock might 
be so soft that wood would not measurably spread, nor lead nor leather 
be made to '-flow" under the pressure which would crush it, and, there- 
fore, that steel, wood, lead, and leather would at some low point give the 
same result. 

Fortunately, this could be reduced to direct experiment. On hand 
were some Sebastopol limestone, {challc,) three cubes of a soft sandstone,, 
and two sets of cubes of Massillon sandstone. These were all tested 
with the following results. (Table III A.) 





Percentage with cush- 
ions of— 




Kind of stone. 


1 


T3 

o 
o 


rt 
^ 




Kemarks. 


Sebastopol limestone or chalk . . 

Drab-colored sandstone 

.Massillon sandstone, Ohio 

Do 


100 

100 
100 

100 


100 

100 
110 

103 


100 

100 
90 

85 


100 

'59." 4' 


Mean of fourteen cubes, 2 inches by 2 inches- 

by 2 inches. 
Mean of three li inch cubes. 
Mean of sixteen cubes, 2 inches by 2 inches- 

by 2 inches. 
Mean of five cubes, 2 inches by 2 inches by 

2 inches. 



The above table shows about equal results with steel and wood, while 
the real crushing-resistance of the stones tested is much below that of 
the granites and marbles before mentioned. 

It seems, then, that with stones of great hardness and toughness com- 
bined, steel and wood give approximately equal results; that with stones 
which, thougii hard, are yet deficient in toughness, the peculiar action of 
the wood-cushions spreading sideways, and thus exerting a strain requir- 
ing tensile resistance, causes the stone to be crushed at a lower figure 
than with steel, which latter, as already stated, tends to bind the stone 
together by its rigidity and frictional resistance to lateral pressure. 
With stones of considerably greater softness, the power of the stone ta 



27 



resist crushing is overcome before sufficient pressure bas been developed 
to bring the action of the wood-fibers on the stone fairly into play. 

Again, we may observe by experiments (Table IV) that when stone is 
in thinner slabs than cubes, greater strength is obtained to the amount 
of 50 per cent, under the pressure of steel. This is not so with wood, 
as may be observed in the same table, and engineers know that it is not 
so in actual work — that there is no remarked advantage nor disadvan- 
tage when the beds are true in each case. 

Now this must be so, because, while the crushing-resistance is un- 
doubtedly increased by thinness in the slab, the tensile resistance is 
decreased by the lessened number of square inches upon which it acts, 
and thus wood, compared with the experience of actual work, again 
asserts its true quantitative relations. 

Wood has also the faculty of exposing the character of stone which 
suffers from "drys'' or slaty cleavage, a fault which is disguised by lead 
and leather on account of their flowage, and by steel from its perfect 
rigidity. 

The experiments, though far from being completed on this particular 
point, indicate a close relation between the beam or transverse strength 
of stone and its tensile strength ; also, that a divergence between the 
compressive results obtained with steel and with wood cushions is accom- 
panied by a corresponding divergence in transverse strength. 

The beam strength of only two varieties of stone was satisfactorily 
tested, the beams being 2 inches by 2 inches in cross- section, broken on 
supports 2J inches apart, with the following results, (Table Y:) 

East Chester, K Y., marble broke at 4,000 to 4,200 pounds. 

Keene, N. H., granite broke at 3,300 pounds. 

The percentages of compressive resistance between steel and between 
wood cushions, for the same kinds of stone, were as follows, (Table III :) 

East Chester marble, 100 for steel, 91 for wood. 

Keene, X. H., granite, 100 for steel, 82.6 for wood. 

This points to the existence of some law which cannot be enunciated 
or deduced without further investigation. It is true that stone is never, 
when it can be avoided, placed in positions where it is subjected to a 
transverse strain. Unequal settlement, however, which can rarely if 
ever be entirely prevented, is certain to produce it, and where great 
disturbance from such cause is to be apprehended, only stone possess- 
ing relatively great beam or transverse strength should be used. 

TABLES OF SUNDRY SPECIAL EXPERIMENTS. 

Table I. — Shoiving the increase, in resistance, per square inch., of cubes of yelloivisTi-grey 
Berea sandstone, as tlie size of the cube is increased. These ivere pressed upon by wooden 
cushion blocks, ranging from one-sixteenth to a little over three-eighths of an inch in thickness, 
as the cubes increased, and of the same bed dimensions as the stone. They were all broken on bed 





A" cube.* 


\" cube.* 


f " cube.* 


1" cube. 


]i" cube. 


l|"cube. 


If" cube. 




260 
300 
330 
350 
300 
250 
300 
400 


1,400 
1,500 
1,700 
1,500 
1,600 
1, 500 
],500 
1,500 
1,500 
1,500 


4,000 
3,100 
3,200 
3,300 
4,000 
3,900 
3,500 


6,800 
6,950 
6,700 
8,200 
7,200 
7,200 
6,200 
7,700 
5,950 


9,200 
13, 450 
11, 200 
10, 200 

9,700 
10, 200 
11,900 

13, 200 

14, 200 


17, 200 
19, 200 

16, 200 
19,200 

19, 700 

17, 000 

20, 200 
19, 400 
17, 800 
19, 200 


29, 200 
33,000 

25, 800 

30, 400 

26, 200 

26, 600 
23, 200 
29, 800 

27, 400 

























Total 


2,490 
312 


15, 200 
1,520 


25. 000 


62, 900 


103, 250 


185, 100 


256, 600 




Average 


3,570 


6,990 


11, 472 


18, 510 


28 510 






Square incli 


4,992 


6,080 


6, 347 


6,990 


7,342 


8, 226 


9,310 





28 



Table I. — Increase, in resistance, per square inch, ^c. — Continued. 





2" cube. 


2i" cube. 


2i" cube. 


2|" cube. 


3" cube. 


4" cube. 




32, 200 
32, 200 

25, 700 

42, 200 

26, 800 

43, 200 
37, 700 
43, 200 
39, 200 


Cracked. 

45, 200 
43, 200 
43, 200 
50, 200 

46, 200 

47, 200 

48, 200 
Cracked. 


53, 200 
50, 200 

52, 200 
66, 200 

53, 200 
57, 200 
65, 200 
50, 200 
50, 700 
55, 200 


75, 200 

69, 200 

74, 200 

68, 200 

70, 200 
74, 200 

69, 200 
78, 200 
84, 200 
81, 200 


94, 200 
90, 200 
89, 000 


187, 500 




















































Total 


322, 400 


323, 400 


553, 500 


744, 000 


273, 400 


187, 500 




Average 


35, 822 


46, 200 


55, 350 


74, 400 


91, 133 


187, 500 






8,955 


9,130 


8,856 


9, 838 


10, 125 


11,720 





* It must be remembered that below a certain point per square inch, say seven or eight thousand 
pounds, the peculiar influence of wood becomes nothing ; the strength of these is therefore relatively 
ncreased. 
i 

Table II. — Showing tlie increase in resistance per square inch of ciibes of blue Berea sand- 
stone, as the size of the cube is increased. These ivere pressed upon by hardened-steel sur- 
faces. They were all broken on bed. 





1" cube. 


li" cube. 


li" cube. 


If" cube. 


2" cube. 


2i" cube. 


2i" cube. 


2|" cube. 




9,400 

12,200 

10,800 

11, 800 

7,800 

10, 200 

7,800 

11, 100 

7,800 

7,800 

7,800 


15, 000 
15, 800 
17, 400 
19, 800 
16, 700 
15, 240 

15, 800 
15, 000 

16, 200 
13, 800 


25, 000 
2«, 600 

19, 800 
0) 

20, 600 
28, 600 
27, 800 
22, 200 
20, 600 


34, 200 

40, 600 
30, 000 

38, 200 
25, 400 

41, 800 
23, 800 
40, 600 

39, 000 


56, 800 
38, 200 
50, 300 
50, 200 
50, 200 
30, 200 
53, 800 
42, 800 
53, 800 
53, 800 


69, 300 
47, 800 
47, 800 
53, 100 
79, 800 

70, 800 
65, 000 
70, 800 
59, 800 
69, 300 


65, 800 

65, 800 
52, 800 
59, 300 

66, 800 
72, 300 
65, 800 

67, 800 
81, 800 


94, 000 
*100, 000 
*100, 000 
*100, 000 

91, 500 

95, 000 
*100, 000 




































Total 


104, .500 


160, 740 


193, 200 


313, 600 


480, 100 


633, 500 


598, 200 








Average 


9,500 


16, 074 


24, 150 


34, 844 


48, 010 


63, 350 


66, 466 


100, 000 


Square inch . . . 


9,500 


10, 300 


10, 730 


11, 377 


12, 000 


12, 500 


10, 635 


13, 200 



* Not broken. Average therefore deduced. 



t Cracked. 



Tables la and Ha. — Showing the calculated ordinates of cuMc parabolas, deduced from th". 
annexed formulas, compared ivith the actual averages obtained by breaking the stone, as 
shown more in detail in Tables I and II. 



Table la. 


Table Ila. 


X 


Value of y de- 
duced from 
calculation. 


Value of y de- 
duced from 
experiment. 


X 


Value of y de- j Value of y de- 
duced from 1 duced from 
calculation. experiment. 


I inch 


4,410 
5,558 
6,356 
7,000 

7, 539 
8,015 

8, 435 
8,820 

9, 170 
9, 499 
9, 807 

10, 095 
11, 112 


4,992 
6, 080 
6,347 

6, 990 

7, 342 

8, 226 
9,310 
8, 955 
9,130 
8, 855 
9,838 

10, 125 
11, 720 


1 inch 


9, 500 
10,231 
10, 877 
11,447 
11,970 
12, 445 

12, 895 

13, 309 




i inch . . . 




1 inch 




1 inch 


9, 500 




IJ inches 

U inches 

l| inches 

2 inches 

2^ inches 

2^ inches 

2i inches 


10, 300 


li inches 

13- inches 


10, 730 
11,377 
12, 000 


2i inches 


12,500 




10, 635 


2J- inches 


13, 200 






4 inches 








3 

y= \^lc .7000 


3 

y= S' X .9300 



29 



Table III. — Showing the resistances in total amount of 2-inch cubes of different hinds of 
stone, and of different qualities of the same Und of stone, under various surfaces of jpress- 
nre. The beds of the granite and marble cubes were rubbed to the border of polish ; those 
of sandstone were rubbed smooth. 



Kind of stone. 


Steel. 


Wood. 


Lead. 


Leather. 




93, 000 
91, 000 
96, 000 
91,000 


89, 000 
100, 000 

88, 000 

89, 000 


68, 000 
66, 000 
60, 000 
57, 700 


















92, 750 


91, 500 


62, 925 








■pprf PTif acrfi .... ..... .. 


100 


98.6 


67.8 








T\rarhl« T^a<5t Chp<?ter !N" Y - . 


80, 000 

*54, 000 

76, 000 

96, 000 


72, 500 

73, 125 

*67, 000 

-68, 000 


47, 000 
51, OiO 

48, 000 
. 39, 000 






















76, 500 


70, 156 


46, 250 








"PprppTitno-ft .. . ...... 


100 


91.7 


62.4 

24, 360 

31, 400 

32, 200 

33, 800 

25, 800 








SonrlefnTip T^prpa miin ClllnisTl-oTflV Tvlrtd) 


42, 600 
54. 000 
39, 480 
41, 800 
47, 240 


42, 600 
45, 000 

37, 000 
42, 600 

38, 600 


26, 600 




26, 800 

27, 240 
27, 000 
27, 000 


.A vera ""G • ..................... •• . .... 


45, 024 


41, 160 


29, 512 


26, 928 






Percenta.£e .. -. ........ 


100 


91.4 


65.5 


59.8 






Keene, X. H., granite, used in inside of new capitol Albany, 
X. Y. 


100, 000 
92, 000 
96, 000 


83. 000 

84, 000 
71, 000 


55, 700 
59, 500 
58, 500 


65, 700 
60, 009 
63, 000 




96, 000 


79, 333 


57, 900 


62, 900 








100 


82.6 


60.3 


65.5 






Vermont marlole Yt .. . - - .. . .. - 


56, 000 
54, 300 
51, 100 
51,100 


42, 600 

43, 400 
45, 000 
42, 600 


37, 960 
37, 650 
39, 400 
32, 200 


27, 200 




31, 400 
34, 600 
37,800 




53, 125 


43, 400 


36, 802 


32, 750 






Percentage 


100 


82 


69.4 


61.6 







*The one nnder steel probably flawed; the two tinder wood slivered. Calcnlating the two wonld 
make the difference in the two columns abont the same, so they were left as recorded on the gauge. 



General average percentages from TaMe III. 



Eand of stone. 


Steel. 


Wood. 


Lead. 


Leather. 


First granite 


100 
100 
100 
100 
100 


98.6 
82.6 
91.7 
82.0 
91.4 


67.8 
60.3 
62.4 
69.4 
65.5 






65.5 


First marble 




Second marble 


6L6 


First sandstone 


59 8 








100 


89.2 


65.1 


62.3 








100 


89.0 


65.0 


62.0 







30 

Table III— A. 



Kind of stone. 


Steel. 


"Wood. 


Lead. 


Leather. 


Limestone, (chalk,) Sebastopol, mean of 14 cubes 2" x 2" x 2", 
all breaking at nearly same. 


4,300 


4,300 


4,300 


4,300 


Percentage 


100 


100 


100 


100 






Sandstone, drab, 3 cubes, H" in all 


9,000 


9,000 


9,000 










100 


100 


100 








Sandatone frnm IVfassilloTij Ohio, Q-inrTi nnhps . . .... 


37, 000 
31. 000 


37, 000 
33, 000 


29, 000 
















34, 000 


35, 000 


29, 000 










100 


103 


85 








Another and softer sandstone from Massillon, Ohio, 2-inch 
cubes. 


29, 800 

*17, 600 
22, 600 
21, 000 


28, 444 

29, 800 
26, 766 
22.600 


17, 800 

23, 400 
25, 080 
21, 720 


13, 000 

14,600 

14, 600 
16, 000 


Average 


22, 640 


26, 901 


22, 000 


14, 550 




Percentage .... 


ioo 


118.8 


97 


64 






* Omitting this result, and the percentage becomes 


100 


110 


90 


59.4 


Sebastopol limestone, in slabs 2j' x 2" x 1" 


4,700 
4.500 


4,900 
4,500 


5,000 
4,700 


4.500 
5,000 


Average 


4,600 


4, 700 


4,850 


4 750 








100 


100 


100 


100 







Table IV. — Showing the resistance of prisms of 'blue Berea sandstone having different 
heights in relation to the width of ted, and droJcen under steel, wood, lead, and leather. 
The tahle is subdivided for convenience of reference in the discussion. The specimens icere 
all taken from one Mock. 





2" X 2" X 1" 


2" X 2" X 2" 


2" X 2" X 4" 


11" X li" X r 


11" X U" X 11" 


11" X 11" X 4" 


f 

Broken between steel J 
cushions "> 


64, 000 
83, 000 
87, 500 
75, 700 
73, 800 
65, 100 
82, 100 


58, 000 
39, 400 
51, 500 
51, 400 
51, 400 
31, 400 
55, 000 
55, 000 


47, 000 
35, 400 

48, 200 
42, 200 
47, 100 


32, 600 

32, 200 
30, 200 
38, 840 

33, 000 
40, 200 
37, 100 
33, 000 


26, 200 
29, 800 
21, 000 
21, 800 
29, 800 
29, 000 
23, 400 
21, 800 


21, 960 
21, 000 
24, 800 

21, 800 

22, 600 








(^ 














Averages 


75, 888 


49, 137 


43, 980 


34, 643 


25, 350 


22, 432 





2" X 2" X 1" 


2" X 2" X 2" 


2" X 2'' X 4" 


2" X 2" X 6" 


■ 


40, 000 

41, 000 

42, 000 
46, 000 
39, 000 
50, 000 
50, 000 
41,000 
49, 000 

44, 000 

45, 000 
55, 000 
52, 000 
44, 000 


46, 000 
45, 000 
45, 000 
44, 000 

43, 000 

44, 000 
40, 000 


37, 000 
40, 200 

33, 800 

34, 600 
40, 200 


41, 000 
40, 200 
40, 200 
39. 400 
34, 600 
39 400 


Broken between wood cushions < 




31 400 














































t 












Averages , . 


45, 571 


43, 857 


37, 160 


38, 028 







31 



Table IY. 


—Besistance of Nue Bei 


-ea sandstone, ^-c— Continued. 






Steel. 


Wood. 


Lead. 


Leather. 


Slabs of 2" X 2" X 1" 


! 


75, 000 
61, 800 
70, 200 
71, 200 


49, 200 
43, 800 
43, 200 
47, 800 


37, 800 
26, 200 

29, 000 

30, 000 


17, 000 
19, 000 
22, 320 
27, 400 


A vera crpa 


69, 550 


47,250 30,750 


21 430 








Percenta "'e 


100 


67.9 


44.2 


30 8 







Table Y. — Beams 2"x 2"x 6" ; bed 6''x 2", resting on pine blocks, and broTcen by xvrougJit-iron 
cylinder f inch diameter across center ; supports 2^ inches apart. 



Granite. 
Millstone Point, Conn. 


Marble. 
East Chester. 


Granite. 
Keene, N. H. 


4,000 to 4,500 


4,000 to 4,200 } 3,300 



Records not fully satisfactory, but sufficiently approximate for relative results. The 
East Chester marble and Keene, N. H., granite records can both be relied on ; those of 
the Millstoue Point granite cannot. 

Table YI. — Showing the difference in resisting power between stones broken tvith wooden- 
cushions — when their beds are polished — and stones ivith same pressing surface when only 
ivorJced to clear beds. 



Kinds of stone. 

• 


PoHshed. 


Unpolished. 


Granite : 

Quincy, Mass 


99, 000 
100, 000 
86, 500 
95, 000 
91, 500 
79, 333 
94, 000 


71.000 


Staten Island, K Y 


89, 000 
.53, 500 
73, 000 


Ganisons N. X ... 


Tarrvtown, X. Y 




75, 000 
51, 000 
71, 000 


Keene, X. H . . . . 


Westerly, E. I 






645, 333 


483, 500 




Marble : 

East Chester, X. Y 


70, 156 
43, 400 


51, 800 


Vermont marble Yt 


35, 000 




Difference 25 per cent (nearly) 


113, 556 


86, 800 





Table Yla. — General average percentage of the crushing-strength for various classes and 
qualities of stones referred to unpolished stones between wood cushions as a standard. 





Polished stone crushed between cush- 
ions of— 




Steel. 


Wood. 


Lead. 


Leather. 




147 


133 


97 


93 








Unpolished stone crushed between cush- 
ions of— 




Steel. 


Wood. 


Lead, j Leather. 


Sandstones and unpolishable stones breaking above 10,000 

pounds per square inch. 
Between 10.000 and 8,000 pounds 


110 
100 
100 
100 


100 
100 
100 
100 


1 
73 1 67 
83 ' 


Between 8.000 and 6,000 pounds 


85 ' 65 


At 1,000 pounds per square inch 


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PLATE 1 . 

EIAGRAM OF CRUSHEl) CUBES OF ST0:NE 



HOMDCJENEOTTS STO^E 



GRAN^ITE 



GRANITE. 
45 




GRANITE. 
46 



BED. 

sandsto:ne 

54 



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-^ PLATE 21. 

DIA6RAM0E CRUSBmG STREKGTHPER SQUAREINCH 

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1% 1 



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Merrill's Iron Trnss Bridges. 

Third Edition. 4to. Qoth. $5.00. 

Ikon Truss Bridges for Railroads. The Method of Calcnlating 
Strains in Trusses, with a careful comparison of the most prominent 
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CoL William E. Merrill, U.S.A., Corps of Engineers. Nine litho- 
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Slireve on Bridges and Roofs. 

8vo, 87 wood-cut lllustrationB. Cloth. $3.50. 

A Treatise on the Strength of Bmdges and Roofs — comprising 
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&om fixed and moving loads, with practical applications and examples, 
for the use of Students and Engineers. By Samuel H. Shrere, A. M., 
CItU Engineer. 

The Kansas City Bridge. 

4to. aoth. $6.00 

With an Account of the Regimen of the Missouri River, — and 
a description of the Methods used for Founding in that River. By O. 
Chanute, Chief Engineer, and George Morison, Assistant Engineer. 
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Clarke's Qnincy Bridge. 

4to. Cloth. $7.60. 

Descriftion of the Iron Railway. Bridge across the Mississippi 
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Cain on Arclies. 

16mo. Cloth extra. |1.75. 

A Practical Treatise on Voussoir and Solid and Braced Arches. By 
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Roebling's Bridges. 

Imperial folio. Cloth. $26.00. 
Loiro AND Short Spax Railway Bridges. By .fohn A. Roebling, 
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8to. 60 Dlufltrations. Cloth. $1.50. 
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New Constructions in Csaphic Statics. By Prof. Henry T. Eddy, C. E., 
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A Treatise on Bracing, — with its application to Bridges and other 
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Stoney on Strains. 

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The Theory op Strains in Girders — and Similar Structures, with 
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Skeleton Structures, especially in their Application to the btdldlag 
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King's Notes on Steam. 

Nineteenth Edition. 8vo. $2.00. 
Lkssons and Practical Notes on Steam, — the Steam Engine, Propel- 
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Link: and. Valve Motions, by W. S. 
Ancliincloss. 

Sixth Edition 8vo. Cloth. $3.00. 
Application of the Slide Valve and Link Motion to Stationary, 
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Bacon's S team-Engine Indicator. 

12mo. Cloth. Si. 00 

A Treatise on the Richards Steam-Engink Indicator, — ^with 
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Isher^wood's Engineering Precedents. 

Two Vols, in One. 8vo. Cloth. $2.60. 

Engineering Precedents for Steam Machinery. — By B. F. Ishkr- 
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Slide Valve by Eccentrics, by Prof. O. W. Mao- 
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Stillraan's Steam-Eiig-iiie Indicator. 

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Collins' Useful Alloys. 

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Groodeve's Steam Engine. 

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Grrnner on Steel. 

8vo. Cloth. $3.50. 

The Manufacture of Steel. By M. L. Gruner ; translated from 
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Hydranlic Mining. 

18mo. Cloth. Bevelled board?. $1.00. 
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Tucker's Sugar Analysis. 

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A Manual of Sugar Analysis. Including the Applications in General of 
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Jones' Organic Oliemistry. 

18mo. Cloth. $1. 

Text-Book of Experimental Organic Chemistry for Students, By H. 
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AttATTOod's Blcvr !Pipe. 

12mo. Cloth extra. $2. 

Practical Blow-Pipe Assaying. By George Attwood. 210 pages. T4 

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Plympton's BloATv^-Pipe Analysis. 

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The Blow-Pipe ; A Guide to its Use in the Determination of Salts andl 
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Brooklyn, N. Y. 



Plattner*s Blo^v-Pipe Analysis. 

Third Edition. Revised. 568 pages.* 8vo> Cloth. $5.00. 

Plattner's Manual op Qualitativb and Quantitative Analy- 
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Pynclioii's OKeraical Physics. 

New Edition. Revised and enlarged. Crown 8vo. Cloth. $3.00. 
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of Trinity College, Hartford. 



Eliot and Storer's Qualitative Clieraical 
Analysis. 

New Edition. Revised. 12mo. Ulustrated. Cloth. $1.50. 

A Compendious Manual op Qualitative Chemical Analysis. 

By Charles W. Eliot and Frank H. Storer. Revised, with 

the cooperation of the Authors, by William Ripley Nichols, 

Professor of Chemistry in the Massachusetts Institute of Technology. 



Rammelsberg's Cliemical Analysis. 

8vo. Cloth. $2,25. 
Guide to a Course op Quantitative Chemical Analysis, 
Especially of Minerals and Furnace Products. Illustrated 
by Examples. By C. F. Rammelsberg. Translated by J. Towlkr, 
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Naqnet's Legal Cliemistry. 

Illustrated. 12mo. Qoth. $2.00. 
iiEGAL Chemistry. A Guide to the Detection of Poisons, Falsifica- 
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the Use of Chemists, Physicians, Lawyers , Pharmacists, and Experts. 
Translated, with additions, including a List of Books and Memoirs 
on Toxicology, etc., from the French of A. Naquet. By J. P. 
Battershall, Ph. D., with a Preface by C F. Chandler, Ph. D., 
M.D.,LL.D. 



Prescott's Qnalitative Cliemistry. 

12mo. Cloth. $1.50. 
First Book in Qualitative Chemistry. By Albert B. Prescott, 
Professor of Organic and Applied Chemistry in the University of 
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D. VAN NOSTRAND. 



Presoott's Proximate Organic Analysis. 

12mo. Cloth. $1.75. 

Outlines of Proximate Organic Analysis, for the Identification, 
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Prescott's Alcoliolic Liqnors. 

12mo. Cloth. §1.50. 
CHE^tfiCAL Examination of Alcoholic Liquors. — A Manual of the 
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Albert B. Prescott, Professor of Organic and Applied Chemistry 
in the University of Michigan. 



Prescott and Donglas's Qnalitative Clieniical 

Analysis. 

Third Edition. Kevised. 8yo. Cloth. S3. 50. 
A Guide in the Practical Study of Chemistry and in the Work of Analysis. 



Mott's Clae mists' Mannal. 

8vo. 650 pages. Qoth. S6.00, 
A Practical Treatise on Chemistry (Qualitative and Quantitative 
Analysis), Stoichiometry, Blowpipe Analysis, Mineralogy, Assaying, 
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Ph.D. 

Beilstein's Ch.eniical Analysis. 

12mo. Cloth. 75c. 
An Introduction to Qualitative Chemical Analysis. By F. Beil- 
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Cald^v^ell & Breneman's Cliemical Practice. 

8vo. Cloth. 188 pages. Illustrated. New and Enlarged edition. Sl,50. 
lyiANUAL OF Introductory Chemical Practice, for the use of Students 
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well and A. A. Breneman, of Cornell University. Second edition, 
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10 SCIENTIFIC BOOKS PUBLISHED BY 

Gillmore's Limes and Cements. 

Fifth Edition. Revised and Enlarged. Svo. Clotk. $4.00. 

Practical Tkeatisk on Limes, Hydraulic Cements, and Mos* 
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Brevet Major-General U. S. Army. 



Gillmore's Coignet Beton. 

Nine Plates, Views, etc. 8vo. Cloth. $2.60. 

Coignet Beton and Other Artificial Stone. — By Q. A. Gill- 
more, Lt.-Col. U. S. Corps of Engineers, Brevet Major-General U.S. 
Army. 

Q-illmore on Roads. 

Seventy Illustrations. 12mo. Cloth. $2.00. 

A Practical Treatise on the Construction of Roads, Streets, 
and Pavements. By Q. A. Gillmore, Lt.-Col. U. S. Corps of 

Engineers, Brevet Major-General U. S. Army. 



Grillmore's Building Stones. 

8vo. Cloth. $1.00. 

Report on Strength of the Building Stones in thb Unitbd 

States, etc. 

HLolley's Railvray Practice. 

1 vol. folio. Cloth. $12.00. 

American and European Railway Practice, in the Economical 
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Coal-buming Boilers, Combustion, the Variable Blast, Vaporization, 
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and the adaptation of Wood and Coke-burning Engines to Coal- 
burning ; and in Permanent Way, including Road-bed, Sleepers, 
Rails, Joint Fastenings, Street Railways, etc., etc. By Alexander 
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I 



Useful Information for Rail^vay Men. 

Pocket form. Morocco, gilt. $2.00. 

Compiled by W. G. Hamilton, Engineer. New Edition, Revised 
and Enlarged. 577 pagea. 



D. VAN NOSTRAND. 11 



Stuart's Civil and Military Engineers o^ 
America. 

cro. niustrated. Cloth. $5.00. 
The Civil and Military Engineers of America. By General 
Charles B. Stuart, Author of " Naral Dry Docks of the United 
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el the most important and original works constructed in America. 



Shook on Steam Boilers. 

^ Quarto. Illustrated. Half morocco. ^15.00. 

Steam Boilers ; their Design, Construction and Management. By Wil- 
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cuts and 36 full page plates (several double). 



Simms' Levelling. 

12mo. Cloth. S2.60. 
A TREATiSE ON THE PRINCIPLES AND PRACTICE OF LEVELLING, 

showing its application to purposes of Railway Engineering and the 
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the fifth London edition, Revised and Corrected, with the addition of 
Mr. Law's Practical Examples for Setting-out Railway Curves. 
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Jeffers' Nautical Surveying. 

niustrated with 9 Copperplates and 31 Wood-cut Illustrations. 8vo. ClotlL $5.00. 
Nautical Surveying. By William N. Jeffebs, Captain U. 3. 
Navy. 

Text-book of Surveying. 

8vo. 9 Lithograph Plates and several Wood-cuts. Cloth. $3.00. 
A Text-book on Sueteying, Projections, and Portable Instruments, 
for the use of the Cadet Midshipmen, at the U. S. Naval Academy. 



The Plane Table. 

Svo. Cloth. S2.00. 

Its Uses in Topoghapeical Susvbyiko. From the papers of tiie 
U. S. Coast S¥»7ey. 



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Chanvenet's Lianar Distances. 

8to. Cloth. $2.00. 
New Method off Correctin-q Lunar Distances, and ImproTftd 

Method of Findirtg the Error and Rate of a Chronometer, by eqtiAl 
altitudes. By Wm. Chauvenet, LL.D., Chancellor of Washingtea 
University of St. Louis. 

Burt's Key to Solar Compass. 

Second Edition. Pocket-book form. Tuck. $2.50. 
Key to the Solar Compass, and Surveyor's Companion ; comprising 
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Linear Surveys and Public Land System of the United States, Notea 
on the Barometer, Suggestions for an Outfit for a Survey of Four 
Months, etc. By W. A. Burt, U. S. Deputy Surveyor. 



Ho^\^ard's Earth. w^ork Mensuration. 

8vo. Illustrated. Cloth. Sl.50. 
Earthwork Mensuration on the Basis of the Prismoidal 
FoRMULJE. Containing simple and labor-saving method of obtaining 
Prismoidal Contents directly from End Areas. Illustrated by 
Examples, and accompanied by Plain Rules for practical uses. By 
Conway R. Howard, Civil Engineer, Richmond, Va. 



Morris' Easy Rules. 

78 niustrations. 8vo. Cloth. $1.50. 
Easy Rules for the Measurement of Earthworks, by means of 
the Prismoidal Formula. By Elwood Morris, Civil Engineer. 



Clevenger's Surveying. 

Illustrated Pocket Form. Morocco, gilt. $2.50. 
A Treatise on the Method of Government Surveying, as 
prescribed by the U. S. Congress and Commissioner of the General 
Land OflBce. With complete Mathematical, Astronomical, and Prac- 
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Students who contemplate engaging in the business of Public Land 
Surveying. By S. V. Clevenger, U. S. Deputy Surveyor. 

He^vTson on Embankments. 

8vo. Cloth. $2.00. 
Principles and Practice of Embanking Lands from River 
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Hkwbon, Civil Engineer. 



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Minifie's Mecliaiiical Drawing. 

Niath Edition. Royal 8vo. Cloth. |4.00. 

A Text-Book of Geometrical Drawing, for the use of Meclianics 
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Elevations of Buildings and Machinery ; an Introduction to Isometri- 
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With over 200 diagrams on steel. By William Minifie, Architect. 
With an Appendix on the Theory and Application of Colors. 



Minifie's Greometrical Ora^ving. 

New Edition. Enlarged. 12mo. Cloth. ^2.00. 

Geometrical Drawing. Abridged from the octavo edition, for th» 

use of Schools. Illustrated with 48 steel plates. 



Free Hand Dra^v^ing. 



Profusely Illustrated. 18mo. Boards. 50centi. 

A Guide to Ornamental, Figure, and Landscape Drawing. By an 
Art Student. 



Tlie Meclianic's Friend. 

12mo. Cloth. 300 Illustrations. $1.60. 
The Mechanic's Friend. A Collection of Receipts and Practical 
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Tools, Instruments, Machines, and Processes connected with th© 
Chemical and Mechanical Arts. By William E. Axon, M.R.S.L. 



Harrison's Meclianic's Tool-Book:. 

44 Illustrations. 12ino. Cloth. $1.60. 
Mechanics' Tool Book, with Practical Rules and Suggestions, for the 
use of Machinists, Iron Workers, and others. By W. B. HarrisoW: 



Randall's Qnartz Operator's Hand-Book. 

12mo. aoth. $2 00. 

Quartz Operator's Hand-Book. By P. M. Randall. New 

edition, Revised and Enlarged. Fully illustrated. 



14 SCIENTIFIC BOOKS PUBLISHED BY 

Joynson on Macliiiie Grearing. 

8vo. Cloth. S2.00. 
The Mechanic'8 and Student's Guide in the designing and Con* 
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Wheels, etc., and the Drawing of Rectilineal and Curved Surface*. 
Edited by Francis H. Joynson. With 18 folded plates. 



Max^rell's Matter and Motion.. 

16mo. Boards. S16 pages. 50c. 
Matter and Motion. By Prof. J. Clark Maxwell. 



Barnes' Submarine Warfare. 

8vo. Cloth. $5.00. 
Submarine Warfare, Defensive and Offensive. Descriptions 
of the various forms of Torpedoes, Submarine Batteries and Torpedo 
Boats actually used in War. Methods of Ignition by Machinery, 
Contact Fuzes, and Electricity, and a full account of experiments 
made to determine the Explosive Force of Gunpowder under Water. 
Also a discussion of the Offensive Torpedo system, its effect upon 
Iron-clad Ship systems, and influence upon future Naval Wars. By 
Lieut.-Com. John S. Barnes, U.S.N. With twenty lithographic 
plates and many wood-cuts. 

Foster's Submarine Blasting. 

4to. Cloth. S3.50. 
Submarine Blasting, in Boston Harbor, Massachusetts — Removal of 
Tower and Corwin Rocks. By John G. Foster, U. S. Eng. and 
Bvt Major-General U. S . Army. With seven plates. 



[Plympton's Aneroid Barometer. 

16mo. Boards, illustrated, 50c. Morocco, $1.00. 
The Aneroid Barometer : Its Construction and Use, compiled from 
several sources. 



Williamson on tlie Barometer. 

4to. Cloth. $15.00. 
On the Use op the Barometer on Surveys and Reconnaw 
SANCES. Part I. — Meteorology in its Connection with Hypsometry. 
Part n. — Barometric Hypsometry. By R. S. Williamson, Bvt 
Lt.-Col. U. S. A., Major Corps of Engineers. With iUustrative tabid 
and engravings. 



D. VAN NOSTBAND. Ifi 

Williamsoii's Meteorological Tables. 

4to. Flexible Qoth. $2.5a 

Practical Tables in Meteorology and Hypsometry, in connection 
with the use of the Barometer. By Col. R. S. Williamson, U.S.A. 



Modern Meteorologv- 

12mo. Cloth. $1.50, 
A Series of Six Lectures, delivered under the auspices of the Me- 
teorological Society in 1878. Illustrated. 



Nugent on Optics. 

12ino. Cloth. 81.50. 



Treatise on Optics ; or, Light and Sight, theoretically and practically 
treated; with the application to Fine Art and Industrial Pursuits. 
By E. Nugent. With 103 illustrations. 



Bo^wser's Analvtic Greometrv. 

12mo. Cloth. $1.75. 
An Elementary Treatise on Analytic Geometry, embracing Plane 
Geometry, and an latroduction to Geometry of Three Dimensions, By 
Edward A. Bowser, Professor of Mathematics and Engineering in 
Rutger's College, New Brunswick, N. J. 



Bowser's Calenlus. 

r2mo. Cloth. $2.2\ 
An Elementary Treatise on the Differential and Integral 
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Author of Treatise on Analytic Geometry. 



Peirce's Analytic Meclianics. 

4to. Cloth. $10.00. 
System of Analytic Mechanics. By Benjamin Peirce, Pro- 
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Craig's Decimal System^ 

Square 32mo. Limp. SOa 

Weights and Measures. An Account of the Decimal System, with 
Tables of Conversion for Commercial and Scientific Uses. By B. F. 
Craig, M.D. 



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Sa^vT^yer's Electric Ijiglitiiig. 

8vo. Clotb. Illustrated. $2.50. 

Electric Lighting by Incandescence, and its Application to Interior 
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liam E. Sawyer. 



Elliot's Eixropean Liglit- Houses. 

51 Engravings and 21 Wood-cuts. 8vo. Cloth. $5.0a 
European Light-House Systems. Being a Report of a Tour of 
Inspection made in 1873. By Major George H. Elliot, U. S. 
Engineers. 

Sweet's Report on Goal. 

With Maps. 8vo. Cloth. $3.00. 
Special Report on Coal. By S. H. Sweet. 



Colbiirn's das "Works of London. 

12nio. Boards. 60 cents. 
Gas "Works of London. By Zerah Colburn. 

^Valker's Scre^v Propnlsion. 

8vo. Cloth. 75 cents. 

Notes on Screw Propulsion, its Rise and History. By Capt. W. H 
Walker, U. S. Navy. 

Pook on SMpbnilding. 

Svo.. Cloth. lUustrated. $5.00. 
Method of Preparing the Lines and Draughting Vessels 
Propelled by Sail or Steam, including a Chapter on La.ying-ofE 
on the Mould-loft Floor. By Samuel M. Pook, Naval Constructor. 

Saeltzer's Acoustics. 

12mo. aoth. $1.00. 
Treatise on Acoustics in connection with Ventilation. By Alex- 
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Eassie on W^ood and its Uses. 

250 Illustrations. Svo. Cloth. $1.50. 
A Hand-book for the Use of Contractors, Builders, Architects, 
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Designs and Estimates. 



W 73 



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